1. Preheat oven to 350 degrees F (175 degrees C). Lightly grease an 8x4 inch loaf pan.
2. In a large bowl, stir together flour, sugar, baking powder, baking soda and cinnamon. Add egg whites, bananas and applesauce; stir just until combined. Pour batter into prepared pan.
3. Bake in preheated oven for 50 to 55 minutes, until a toothpick inserted into center of loaf comes out clean. Turn out onto wire rack and allow to cool before slicing.